Some of the causes of the Russian Revolution were tied to World War I. However, we cannot say that all of them were. It is probably more accurate to say that WWI acted as a catalyst, causing the revolution to happen sooner than it otherwise might have.
The real roots of the Russian Revolution had little to do with WWI. Many people in Russia had, for a long time, felt very oppressed. Russia had one of the least free political systems in Europe. It had a relatively autocratic tsar and essentially no popular control of government. Russia also had a rather backwards and oppressive economic system. Because of these facts, many people in Russia wanted to overthrow their government and create a new system. This had led to attempts at revolutions long before WWI.
However, WWI did help to hasten the Russian Revolution. It did this by weakening Russia very badly. Russia was not really economically strong enough to engage in this total war. The war caused major strains in the economy. The strains made many people even angrier with the government. They protested about things like working conditions in war factories and about food shortages. The government’s resources were stretched thin and it could not put down the unrest. Therefore, the unrest built up momentum until the revolution occurred.
One final connection comes from the role of Germany in the Russian Revolution. Vladimir Lenin, the communist leader, had been exiled in Switzerland. Hoping to stir up trouble in Russia, the German government helped him to return to Russia. Once there, Lenin helped to push for revolution.
In these ways, the causes of the Russian Revolution were tied to WWI, but it is not accurate to say that WWI was the main cause of that revolution.
I wanted to add to pohnpei397's answer. The Russian Revolution was a response to the oppression politically and economically of the people by the government. In World War I, Russia was doing horrendously in the war. The soldiers were sent into battles ill-equipped - no weapons, limited clothing, limited food - and the officers were terrible in tactics. Russia did not have the industries or food productions to supply their front line. Back at home, again, food was limited and many people starved. Tsar Nicholas II (besides setting up a fake legislative - he dissolved it whenever it did something he hated) decided to go out on the front line himself, which connected him to the failures of the war effort, instead of giving himself a scapegoat for the loss (his generals). Now, the people could blame him, and they gladly did so. At home, the people hated his wife, who was German (they were fighting the Germans) and they believed that she was in some conspiracy for their losses. Not to mention, that she trusted Rasputin, a monk, who could somehow cure Alexei, their son who suffered from hemophilia, and the people hated him and the amount of power he held. So after the Russians had enough, they overthrew the tsar and his family.
What the Russian people really wanted was to get out of the war and food to eat. Lenin, the Bolshevik leader, advocated three points: "Peace, land, bread." And the people flocked to him.